Add the first Julia implementations of some of the utility functions

Utilities/Generic/Julia/Utils.jl

+"""
+This is the module with the Julia implementations of the generic utilities of the IN-NOVA project.
+--------------------------------------------------
+Author: Achilles Kappis
+e-mail: axilleaz@protonmail.com
+
+Date: 10/08/2024 (DD/MM/YYYY)
+
+Copyright: MIT
+--------------------------------------------------
+
+# Functions included
+- stepFunc
+- isEven
+- isOdd
+- rotMat3d
+--------------------------------------------------
+"""
+module Utils
+
+
+
+"""
+Numerical (simple) Heaviside function
+--------------------------------------------------
+Author: Achilles Kappis
+e-mail: axilleaz@protonmail.com
+
+Date: 10/08/2024 (DD/MM/YYYY)
+
+Copyright: MIT
+--------------------------------------------------
+Functionality: A Heaviside numerical (step) function
+--------------------------------------------------
+# Input
+
+x::Real: The argument of the function.
+
+zeroHalf::Bool (Optional): The way x = 0 is treated. If this argument is true, the returned value is 0.5 when x = 0, otherwise it is 1. [Default: false].
+
+--------------------------------------------------
+# Output
+result::Float64: Either 0 or 1 based on whether the argument of the function is greater or equal to zero.
+--------------------------------------------------
+# Notes
+
+--------------------------------------------------
+"""
+function stepFunc(x::Real; zeroHalf::Bool = false)
+    if zeroHalf && x == 0
+        result = 0.5
+    else
+        result = x >= 0
+    end
+    
+    return convert(Float64, result)
+end
+
+
+
+
+
+"""
+Determine whether a number is even
+--------------------------------------------------
+Author: Achilles Kappis
+e-mail: axilleaz@protonmail.com
+
+Date: 10/08/2024 (DD/MM/YYYY)
+
+Copyright: MIT
+--------------------------------------------------
+Functionality: Function to check if a real integer is even.
+--------------------------------------------------
+# Input arguments
+
+num::Integer: The number to check.
+
+--------------------------------------------------
+# Output arguments
+
+result::Bool: True if the number is even, False else.
+
+--------------------------------------------------
+# Notes
+
+--------------------------------------------------
+"""
+function isEven(num::Integer)
+    return mod(num, 2) == 0
+end
+
+
+
+
+"""
+Determine whether a number is odd
+--------------------------------------------------
+Author: Achilles Kappis
+e-mail: axilleaz@protonmail.com
+
+Date: 10/08/2024 (DD/MM/YYYY)
+
+Copyright: MIT
+--------------------------------------------------
+Functionality: Function to check if a real integer is odd.
+--------------------------------------------------
+# Input arguments
+
+num::Integer: The number to check.
+
+--------------------------------------------------
+# Output arguments
+
+result::Bool: True if the number is even, False else.
+
+--------------------------------------------------
+# Notes
+
+--------------------------------------------------
+"""
+function isOdd(num::Integer)
+    return mod(num, 2) != 0
+end
+
+
+
+
+"""
+Calculate a 3D rotation matrix
+--------------------------------------------------
+Author: Achilles Kappis
+e-mail: axilleaz@protonmail.com
+
+Date: 10/08/2024 (DD/MM/YYYY)
+
+Copyright: MIT
+--------------------------------------------------
+Functionality: Calculate a 3D rotation matrix.
+--------------------------------------------------
+# Input
+
+xAng::Real: Rotation angle around the x-axis.
+
+yAng::Real (Optional): Rotation angle around the y-axis. [Default: 0].
+
+zAng::Real (Optional): Rotation angle around the z-axis. [Default: 0].
+
+deg::Bool (Optional) [keyword]: This value declares if the provided angles are in degrees or not. If not, radians are assumed. [Default: false].
+--------------------------------------------------
+# Output
+
+rotMat::Matrix{Real}: A 3x3 matrix which applies the rotation.
+
+xRotMat::Matrix{Real}: A 3x3 matrix which applies the rotation around the x-axis.
+
+yRotMat::Matrix{Real}: A 3x3 matrix which applies the rotation around the y-axis.
+
+zRotMat::Matrix: A 3x3 matrix which applies the rotation around the z-axis.
+--------------------------------------------------
+# Notes
+
+--------------------------------------------------
+"""
+function rotMat3d(xAng::Real, yAng::Real = 0, zAng::Real = 0; deg::Bool = false)
+    # Check for units of the angles
+    if deg
+        xAng = deg2rad(xAng)
+        yAng = deg2rad(yAng)
+        zAng = deg2rad(zAng)
+    end
+    
+    # Generate the respective matrices
+    xRotMat = [1 0 0; 0 cos(xAng) -sin(xAng); 0 sin(xAng) cos(xAng)]
+    yRotMat = [cos(yAng) 0 sin(yAng); 0 1 0; -sin(yAng) 0 cos(yAng)]
+    zRotMat = [cos(zAng) -sin(zAng) 0; sin(zAng) cos(zAng) 0; 0 0 1]
+    
+    # Calculate the "total" matrix
+    rotMat = xRotMat * yRotMat * zRotMat
+    
+    # Return
+    return rotMat, xRotMat, yRotMat, zRotMat
+end
+
+
+
+
+end # Module end